Method of quantifying soil carbon

ABSTRACT

One aspect of the present disclosure relates to a method of quantifying soil carbon in a unit of land. The method generally comprises the steps of (i) obtaining an estimated spatial distribution of carbon content in the unit of land, (ii) stratifying the unit of land into a plurality of strata based at least partly on the spatial distribution of carbon content, (iii) selecting one or more locations from each of one or more of the plurality of strata, the one or more locations being selected with randomness, (iv) determining sample carbon content associated with the one or more first locations and (v) determining total carbon content in the unit of land based at least partly on the sample carbon content. In another aspect, this method may be used to quantify soil carbon sequestered in a unit of land by repeating steps (iv) and (v) at a second time and thereafter determining the amount of carbon sequestered. Furthermore, in quantifying the soil carbon sequestered, steps (ii) and (iii) may also be repeated at the second time after re-stratification of the unit of land based on sample carbon determined at the first time.

PRIORITY CLAIM

This application is a national stage application of PCT/AU2011/000702,filed on Jun. 6, 2011, which claims the benefit of and priority toAustralian Patent Application No. 2010902472, filed on Jun. 4, 2010, theentire contents of which are each incorporated by reference herein.

BACKGROUND

In the context of carbon emissions offset trading schemes there is aneed for a statistically and economically viable method for the auditingof soil carbon change over a designated time period for a unit of land.This facilitates transparency in the emitter sequesterer contracts andprovides confidence to the market, the general public and thegovernment.

One method suggested by the NSW Department of Environment, ClimateChange and Water (DECCW) for obtaining such an estimate is the quadratmethod. For a given or designated unit of land, a 25 m by 25 m subareais chosen and divided into 10 by 10 equal sized quadrats. Ten samplesare chosen at random from these 100 quadrats and the carbonconcentration and soil bulk density estimated to a fixed depth ofusually 50 cm. At some later date the process is repeated in the samesubarea. The difference in carbon content is calculated.

The quadrat method has two drawbacks. First, the sampling area (that is,the subarea) is known, potentially leading to fraudulent practices wherecarbon may be deliberately sequestered in the known sampling area. Moreimportantly, the extrapolation of the average carbon content from thesmaller subarea to the larger unit of land under sequestrationmanagement leads to a large sampling variance resulting in an uncertainestimate of the change in carbon content.

SUMMARY

The present disclosure relates generally to a method of quantifying soilcarbon, and particularly to a method of quantifying soil carbon based ona sampling strategy.

According to a first aspect of the present disclosure there is provideda method of quantifying soil carbon in a unit of land, the methodcomprising the steps of:

-   -   obtaining an estimated spatial distribution of carbon content in        the unit of land;    -   stratifying the unit of land into a plurality of strata based at        least partly on the spatial distribution of carbon content;    -   selecting one or more locations from each of one or more of the        plurality of strata, the one or more locations being selected        with randomness;    -   determining sample carbon content associated with the one or        more locations; and    -   determining total carbon content in the unit of land based at        least partly on the sample carbon content.

According to a second aspect of the disclosure there is provided amethod of quantifying soil carbon sequestered in a unit of land, themethod comprising the steps of:

-   -   obtaining an estimated spatial distribution of carbon content in        the unit of land;    -   stratifying the unit of land into a plurality of strata based at        least partly on the spatial distribution of carbon content;    -   selecting one or more first locations from each of one or more        of the plurality of strata, the one or more first locations        being selected with randomness;    -   determining at a first time, first sample carbon content        associated with the one or more first locations;    -   determining first total carbon content in the unit of land based        at least partly on the first sample carbon content;    -   selecting one or more second locations from each of one or more        of the plurality of strata, the one or more second locations        being selected with randomness;    -   determining at a second time, second sample carbon content        associated with the one or more second locations;    -   determining second total carbon content of the unit of land        based at least partly on the second sample carbon content; and    -   determining an amount of sequestered carbon in the unit of land        between the first time and the second time.

According to a third aspect of the disclosure there is provided a methodof quantifying soil carbon sequestered in a unit of land, the methodcomprising the steps of:

-   -   obtaining an estimated spatial distribution of carbon content in        the unit of land;    -   stratifying the unit of land into a plurality of strata based at        least partly on the spatial distribution of carbon content;    -   selecting one or more first locations from each of one or more        of the plurality of strata, the one or more first locations        being selected with randomness;    -   determining at a first time, first sample carbon content        associated with the one or more first locations;    -   determining first total carbon content in the unit of land based        at least partly on the first sample carbon content;    -   re-stratifying the unit of land into a plurality of        re-stratified strata based at least partly on the first sample        carbon content;    -   selecting one or more second locations from each of one or more        of the plurality of re-stratified strata;    -   determining at a second time, second sample carbon content        associated with the one or more second locations;    -   determining second total carbon content in the unit of land        based at least partly on the second sample carbon content; and    -   determining an amount of sequestered carbon in the unit of land        between the first time and the second time.

In various embodiments, the step of obtaining a spatial distribution ofcarbon content includes the step of obtaining a regional prediction ofspatial distribution of carbon content. Alternatively or additionallythe step of obtaining an estimated spatial distribution of carboncontent includes the step of obtaining an estimated spatial distributionof carbon content based at least partly on information associated withthe unit of land. Still alternatively or additionally the step ofobtaining an estimated spatial distribution of carbon content includesthe step of obtaining an estimated spatial distribution of carboncontent based at least partly on any one or more of terrain information,gamma radiometric information, climate information, geologicinformation, regolith information, land use classification informationand known soil carbon information associated with the unit of land.

In various embodiments, the method further comprises the step ofdownscaling the information associated with the unit of land.

In various embodiments, the step of determining sample carbon contentincludes the step of measuring the sample carbon content as measuredsample carbon content. In one such embodiment, the step of measuring thesample carbon content includes the step of measuring the sample carboncontent by combustion of soil at the one or more locations.Alternatively the step of measuring the sample carbon content includesthe step of measuring the sample carbon content by near infraredspectroscopy analysis of soil at the one or more locations.

In various embodiments, the step of measuring the sample carbon contentincludes the step of correcting the measured sample carbon content forinorganic carbon in the soil.

In various embodiments, the step of determining sample carbon contentincludes the step of determining sample carbon content in one or morelayers of measured mass of soil over a determined area of the unit ofland. In one such embodiment, the step of determining sample carboncontent includes the step of spline fitting the measured sample carboncontent in three or more layers of measured mass of soil. Alternativelythe step of determining sample carbon content includes determiningsample carbon content based on the maximum measured sample carboncontent.

In various embodiments, the step of determining sample carbon contentincludes the step of determining composite carbon content from two ormore of said locations. Alternatively the step of determining samplecarbon content includes the step of determining non-composite carboncontent at each of said locations. In one such embodiment, the step ofdetermining composite carbon content from two or more of said locationsincludes the step of compositing respective two or more layers of equalmass of soil from the two or more of said locations.

In various embodiments, the step of determining sample carbon contentincludes the step of determining sample carbon content by absolute,percentage or fractional weight or mass of carbon.

In various embodiments, the step of determining sample carbon contentincludes the step of determining any one or more of the average,variance and standard error of the sample carbon content across the oneor more locations for each of the plurality of strata or re-stratifiedstrata.

In various embodiments, the step of determining sample carbon contentincludes the step of determining any one or more of the cutting shoediameter, push depth, pulled core length and hole depth associated withthe measured mass of soil.

In various embodiments, the step of determining total carbon contentincludes the step of determining total carbon content in a predeterminedmass of soil per unit area of the unit of land. In one such embodiment,the step of determining total carbon content includes the step ofdetermining total carbon content in 1500 kilograms of soil per squaremeter of the unit of land.

In various embodiments, the step of determining total carbon contentincludes the step of determining total carbon content in a predeterminedmass of soil per unit area of the unit of land based at least partly onthe measured mass and the determined area.

In various embodiments, the step of determining total carbon contentincludes the step of determining any one or more of the variance,standard error, a confidence interval, a minimum detectable differenceof the total carbon content in the unit of land.

In various embodiments, the step of determining an amount of sequesteredcarbon includes the step of determining a difference between the firsttotal carbon content and the second total carbon content.

In various embodiments, the method further comprises the step ofdetermining a variance, standard error or confidence interval of thesequestered carbon. In one such embodiment, the step of determining avariance, standard error or confidence interval of the sequesteredcarbon includes the step of determining a variance, standard error orconfidence interval of the sequestered carbon based at least partly onthe variance or standard error of the first sample carbon content and/orthe variance or standard error of the second sample carbon content.

In various embodiments, the first time and the second time are separatedby a period based at least partly on a carbon sequestration contract.

In various embodiments, the first time and the second time are separatedby a period of approximately 5 years apart.

In various embodiments, the first time and the second time are separatedby a period based at least partly on the minimum detectable differenceof the first total carbon content in the unit of land.

In various embodiments, the step of stratifying the unit of land into aplurality of strata includes the step of stratifying the unit of landinto a designated quantity or number of strata. In one such embodiment,the designated quantity or number of strata is based at least partly onany one or more of diversity of landscape, land use type, total area,and allowable uncertainty in quantifying the first total carbon content.

In various embodiments, the step of re-stratifying the unit of land intoa plurality of re-stratified strata includes the step of re-stratifyingthe unit of land into a designated quantity or number of re-stratifiedstrata. In one such embodiment, the designated quantity or number ofre-stratified strata is based at least partly on any one or more ofdiversity of landscape, land use type, total area, and allowableuncertainty in quantifying the second total carbon content.

In various embodiments, the designated quantity or number of strataand/or the designated quantity or number of re-stratified strata are inthe range of five to seven.

In various embodiments, the step of stratifying the unit of land into aplurality of strata includes the step of determining one or more stratumboundaries between the designated quantity or number of strata. In onesuch embodiment, the step of determining the one or more stratumboundaries includes the step of determining the one or more stratumboundaries based at least partly on the spatial distribution of carboncontent. In one such embodiment, the step of determining the one or morestratum boundaries includes the step of determining the stratumboundaries based at least partly on a cumulative function of the squareroot of frequencies of occurrence of carbon derived from the spatialdistribution of carbon content.

In various embodiments, the step of re-stratifying the unit of land intoa plurality of re-stratified strata includes the step of determining oneor more re-stratified stratum boundaries between the designated quantityor number of re-stratified strata. In one such embodiment, the step ofdetermining the one or more re-stratified stratum boundaries includesthe step of determining the one or more re-stratified stratum boundariesbased at least partly on the first sample carbon content. In one suchembodiment, the step of determining the one or more re-stratifiedstratum boundaries includes the step of determining the re-stratifiedstratum boundaries based at least partly on a cumulative function of thesquare root of the frequencies of occurrence of carbon derived from thefirst sample carbon content.

In various embodiments, the step of determining one or more stratumboundaries includes the step of determining one or more optimum stratumboundaries under Neyman allocation.

In various embodiments, the step of determining one or morere-stratified stratum boundaries includes the step of determining one ormore optimum re-stratified stratum boundaries under Neyman allocation.

In various embodiments, the step of selecting one or more locationsincludes the step of determining a designated quantity or number oflocations. In one such embodiment, the step of determining a designatedquantity or number of locations includes the step of determining adesignated number of locations based at least partly on the designatednumber of strata or re-stratified strata. In one such embodiment, thestep of determining a designated quantity or number of locationsincludes the step of determining a designated quantity or number oflocations to be one greater than the designated quantity or number ofstrata or re-stratified strata. In one such embodiment, the step ofdetermining a designated quantity or number of locations includes thestep of determining a designated quantity or number of locations to betwo greater than the designated quantity or number of strata orre-stratified strata.

In various embodiments, the step of selecting one or more locationsincludes the step of selecting one or more locations via randomsampling.

In various embodiments, the step of selecting one or more locationsincludes the step of selecting one or more locations from a samplinggrid of locations being spaced apart by approximately 5 meters.

In various embodiments, the step of determining sample carbon contentincludes the step of determining sample carbon content to a samplingdepth of approximately 1 meter.

In various embodiments, the unit of land includes a farm area or acatchment area.

In various embodiments, the unit of land includes a unit of land of asize between approximately 400 and approximately 3000 hectares.

In various embodiments, the carbon includes either or both of organiccarbon and inorganic carbon.

In various embodiments, the carbon includes any one or more of elementalcarbon, carbon oxides and carbonates.

In various embodiments, the soil includes air-dry soil and/or oven-drysoil.

Additional features and advantages are described in, and will beapparent from the following Detailed Description and the figures.

BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS

FIG. 1 is a flowchart illustrating an embodiment of the method accordingto the present disclosure.

FIG. 2A are examples of landscape variables from gamma radiometrics (twoleftmost columns) and attributes derived from an elevation model (tworightmost columns).

FIG. 2B is an exemplary spatial distribution of percentage topsoilorganic carbon in Australia.

FIG. 2C are examples of primary divisions in the land use classificationfor soil carbon response.

FIG. 2D are details of the primary divisions shown in FIG. 2C.

FIG. 2E is an example of a unit of land being divided into the primarydivisions shown in FIG. 2C.

FIG. 2F is an example of prior or known soil carbon observations forconstructing the prediction function for soil organic carbon.

FIG. 2G is an example of estimated or predicted spatial distribution ofsoil organic carbon (kg⁻¹ m⁻³) in the unit of land shown in FIG. 2E.

FIG. 3 is an example of stratification of (left) and selected locationsin (right) the unit of land shown in FIG. 2E based on the estimated orpredicted soil carbon distribution shown in FIG. 2G.

FIGS. 4A, 4B and 4C is a table showing a summary of variables used incalculation examples.

FIG. 5A is a table showing processed data of core ID “2 i” calculated inExample 1.

FIG. 5B is a graph plotting cumulative soil mass against cumulativecarbon content in Example 1.

FIG. 5C is a table showing processed data of two strata calculated inExample 1.

FIG. 5D is a table showing processed data of the unit of land calculatedin Example 1.

FIG. 6A is a table showing processed data of composited cores ID “2 a”and “2 i” calculated in Example 2.

FIG. 6B is a graph plotting cumulative soil mass against cumulativecarbon content in Example 2.

FIG. 6C is a table showing processed data of two strata calculated inExample 2.

FIG. 6D is a table showing processed data of the unit of land calculatedin Example 2.

FIG. 7A is a table showing processed data of core ID “2 i” calculated inExample 3.

FIG. 7B is a graph plotting cumulative soil depth against cumulativecarbon content in Example 3.

FIG. 7C is a table showing processed data of two strata calculated inExample 3.

FIG. 7D is a table showing processed data of the unit of land calculatedin Example 3.

FIG. 8A is a table showing processed data in calculated in Example 4.

FIG. 8B is a table showing processed data of two strata calculated inExample 4.

FIG. 8C is a table showing processed data of the unit of land calculatedin Example 4.

DETAILED DESCRIPTION

This present disclosure relates generally to a method of quantifyingsoil carbon, particularly soil organic carbon (SOC), in a unit of land.The method may be suited to a farm area or similar landscape ofapproximately 400 to approximately 3000 hectares. The method may beapplicable to smaller and larger areas such as catchment areas. Themethod may be part of a soil carbon auditing protocol, in which changesin the soil carbon over a period of time may be determined byquantifying the soil carbon at the start (time t₁) and the end (time t₂)of that period. The changes in the soil carbon may be determined as thedifference between the soil carbon at t₁ and the soil carbon at t₂, andmay be attributed to the amount of sequestered carbon in the unit ofland over that period. The soil carbon auditing protocol may be used to,for example, verify a carbon sequestration contract. This soil carbonauditing protocol is intended to enable the ascription of carbon creditsto the soil body within a defined area for a defined period. Implicitwithin this style of auditing protocol is that it is time dependant andpost event. That is, sequestered SOC may be verified for a given ordesignated period and traded on the basis of the agreed value to theatmosphere of that period. Such a validation system does not, in itself,offer validation of permanent or perpetual sequestration since thetarget variable is total carbon or total organic carbon, and not anundefined long-lived carbon fraction.

Referring now to the example embodiments of the present disclosureillustrated in FIGS. 1 to 8C, as shown in FIG. 1 , the method ofquantifying soil carbon generally comprises the steps of (i) obtaining aspatial distribution of carbon content in the unit of land, (ii)stratifying the unit of land into a plurality of strata based at leastpartly on the spatial distribution of carbon content, (iii) selectingone or more first locations from each of one or more of the plurality ofstrata, (iv) determining at a first time first sample carbon contentassociated with the one or more first locations, and (v) determiningfirst total carbon content in the unit of land based at least partly onthe first sample carbon content. The first locations should be selectedwith randomness, for example by randomly sampling or other samplingtechniques with stochasticity, to avoid fraudulent practices, such asdeliberate sequestration of carbon at known or predetermined locations.

Steps (i) to (v) above relate to quantification of the soil carbon attime t₁ for determining, for example, the baseline carbon content. Toquantify the soil carbon at time t₂, and hence determining the changesin the soil carbon over the period between t₂ and t₁, the method mayfurther comprises the steps of (vi) selecting one or more secondlocations from each of one or more of the plurality of strata, (vii)determining at a second time second sample carbon content associatedwith the one or more second locations, and (viii) determining secondtotal carbon content of the unit of land based at least partly on thesecond sample carbon content.

Like the first locations, the second locations may be selected withrandomness. Additionally, they may be selected independent of the firstlocations (for example, not repeating the randomly selected firstlocations as the second locations) to avoid fraudulent practices.

The second time may be separated from the first time by a perioddetermined by carbon sequestration contract, for example 5 years. Theseparation period may also be determined based on the minimum detectabledifference associated with the first sample carbon content. For example,if the variance or standard error of the first sample carbon content islarge, a longer separation period may be more sensible, since the carbonsequestered in a short period may be well under the minimum detectabledifference.

The stratification for the soil carbon quantification at time t₂ may bebased on the carbon content quantified at t₁, instead of the spatialdistribution of carbon content obtained prior to or immediately prior tothe soil carbon quantification at time t₁. Therefore steps (vi) to(viii) above may be replaced by the steps of (vi) re-stratifying theunit of land into a plurality of re-stratified strata based at leastpartly on the first sample carbon content, (vii) selecting (withrandomness) one or more second locations from each of one or more of theplurality of re-stratified strata, (viii) determining at a second timesecond sample carbon content associated with the one or more secondlocations, and (vi) determining second total carbon content in the unitof land based at least partly on the second sample carbon content.

Obtaining a Spatial Distribution of Carbon Content

In order to construct the initial stratification for time t₁, thespatial distribution or map of soil carbon of the unit of land may beobtained by predicting or estimating the spatial distribution based atleast partly on information associated with the unit of land. Theprediction or estimation may be constructed using stepwise regression,or other models such as network approaches, from inputs such as:

-   -   common terrain attributes derived from a DEM (Digital Elevation        Model);    -   gamma radiometrics;    -   a specific landuse classification for SOC behaviour;    -   various regional (250-1000 m resolution) climatic, texture and        regolith layers;    -   broad scale (250-1000 m resolution) regional SOC predictions;        and    -   prior or known SOC, or total SOC surveyed from other locations.

Generation of a soil carbon prediction for the unit of land is intendedto incorporate the correlation of all available variables with soilcarbon distribution into a single stratification variable—in this casethe soil carbon prediction function itself. The primary reasoning behindthis approach is that it avoids the troublesome drawback of traditionalhierarchical ‘monothetic’ divisions (i.e., where each division is madein terms of a single variable beginning with the highest correlated tothe lowest, which quickly leads to excessive and disjointed strata).

As a result, we use a single stratification variable: the carbon contentas predicted by an appropriate model that can be applied to the class offarms for carbon auditing, resulting in ‘polythetic’ division. Thereasoning behind this approach is that this predictor can capture theall available prior knowledge, not only about the spatial variation ofthe input variables, but also their relationship with carbon content aswell. Typically a step-wise linear regression model is adopted to carryout this procedure. It should be appreciated that the target variablefor prediction may be varied with respect to the nature and extent ofthe available known carbon data within a particular locale (i.e.,constructed for total organic carbon density, total carbon %, totalorganic carbon % to a variety of spatial or mass coordinates).

Typical input variables publically available for the main Australianagricultural regions include the joint METI and NASA ASTER GlobalDigital Elevation Model V001 and its derived terrain attributes (at 30 mresolution) and the Radiometric Map of Australia (at 100 m resolution);examples of which are depicted in FIG. 2A. In addition, other sources ofinformation such as the topsoil and subsoil SOC % estimation (FIG. 2B)as well as climatic layers from the Australian Soil Resource InformationSystem (ASRIS) dataset (ranging from 250 to 1000 m resolution) may alsoprove useful given that a wide enough spatial range of carbonobservations are used to generate the carbon prediction map.

An approach to land use classification in regards to SOC behavior hasalso been developed with divisions of land use classes based on acombination of known management effects on soil carbon levels and expertknowledge. The primary divisions used are: excluded lands; irrigatedlands; dryland annuals; perennials with inputs and perennials withirregular inputs. A summary of the primary divisions used in this systemis depicted in FIG. 2C with examples of these divisions offered in FIG.2D. A spatial application of this classification is depicted in FIG. 2E.It should be appreciated that within the primary divisions it ispossible to create sub-divisions to accommodate land uses such as treedominated or pasture dominated perennial systems, or full tillage vsno-till dryland annual system, so that the system can evolve withincreasing land use information and general system complexity. However,this process will only increase efficiency up to point, after which thedivisions become too fine and its usefulness as a predictor decreases.In practice this level is determined on a case by case basis and largelyrelies on expert knowledge.

Prior or known soil carbon information may be required to construct asoil carbon prediction map in order to map the ‘best guess’ at thedistribution of soil carbon within the unit of land. An example of thisprior information is provided in FIG. 2F. The relevant variables foreach carbon observation may then be extracted from each variable layerbased on spatial proximity in order to develop the soil carbonprediction function, which, in this instance was performed usingstep-wise regression. This particular spatial prediction function relieson relationships between an index for water accumulation in thelandscape, the type of land use and the ratio of uranium to thoriumwithin the soil/regolith. This relationship is then used to predict thesoil carbon distribution across the unit of land as depicted in FIG. 2G.It should be appreciated that this prediction function need onlyrepresent the ‘best available’ prediction of soil carbon spatialdistribution from the available data, as this process is about combiningprior information into a single variable to allow polythetic division asthe basis of stratification.

Furthermore the above inputs are often available at a coarse resolution.It is envisaged that the use of a downscaling process by, for example,either mechanistic or empirical functions, may transfer the inputs ordata to a finer resolution and hence provide a more finely gridded orrepresentative prediction or estimation of soil carbon. In oneembodiment, the downscaling process utilizes a regional prediction ofsoil carbon distribution (nominally at 250 m resolution) and a computeralgorithm to disaggregate regional carbon predictions using finer scalecovariates (nominally at 30 m resolution) whilst preserving the soilcarbon estimate made at the regional level over the target area. Thecomputer algorithm iteratively employs weighted Generalised AdditiveModels (GAMs) to redistribute the soil carbon estimate onto availablefiner scale covariates that have some relationship with soil carbondistribution. An iterative algorithm of GAM fitting and adjustmentattempts to optimize the downscaling to ensure that the target variablevalue given for each coarse grid cell equals the average of all targetvariable values at the fine scale in each coarse grid cell. In addition,it may be assumed that there is an element of uncertainty (from a rangeof different sources) in the data that is being downscaled. To handlethis uncertainty in the downscaling process, higher weighting may begiven to information which is more accurate than to information that isless accurate. The outcome of the downscaling process may provide soilcarbon information on a finer scale necessary for the stratificationprocedure in accordance with this disclosure.

Stratification

The predicted distribution of soil organic carbon may be used forstratification of the unit of land to, for example, develop a stratifiedsimple random sample. The purpose of this stratification is to partitionthe known variation of soil carbon distribution into the samplingdesign—an approach referred to as a design-based approach to sampling asopposed to a model-based approach to sampling. The implication ofutilizing a design-based (as opposed to model-based) approach tosampling design is that actual values are considered spatially fixed andsampling points are random (model based approaches reverse theseassumptions). This ensures that repeat sampling (through time) isindependent and can therefore be used as a monitoring system whilstsimultaneously providing verification of SOC storage through time.

The quantity or number of strata is generally determined or designatedin the region of 5 to 7 given that the carbon prediction model may notbe too accurate (i.e., R²<0.9). The quantity or number of strata may bedesignated based on the diversity of the landscape, land use types,total area and the level of investment directed towards reducing theuncertainty in determining the total carbon content or carbonsequestered. Where larger properties are targeted (i.e., >2000 ha),higher quality prior data is accessible, or additional funds areavailable to increase the confidence in estimates it is possible toincrease the quantity or number of strata used.

Once the quantity or number of strata has been determined or designated,stratum boundaries between the strata may be determined using the ‘cum√f’ rule. Using the predicted spatial distribution of soil carboncontent for the unit of land, the stratification cut-off levels (whichthen determine the stratum boundaries) can be optimized for a given ordesignated quantity or number of strata by applying the ‘cum √f’ rule.This is the cumulative function of the square root of the frequencies ofcarbon occurrence from the predicted spatial distribution. The spatialdistribution may be nominally divided into approximately 100 bins, whichare then equally divided on the basis of quantity or number of strata.Internal boundaries are then converted back into original carbon unitsand used as the subsequent stratum break points. Stratification underthe ‘cum √f’ rule is close to optimal for Neyman allocation. FIG. 3(left) depicts an example of the stratification of a unit of land intosix strata based on the predicted spatial distribution shown in FIG. 2G.

Re-stratification, if necessary, of the unit of land at time t₂ mayfollow similar stratification steps above. The quantity or number ofre-stratified strata may be determined or designated based on the samplecarbon content determined at time t₁. Similarly re-stratified stratumboundaries may be determined by the ‘cum √f’ rule applied to the samplecarbon content determined at time t₁, instead of the predicted spatialdistribution of carbon content. In one embodiment, after obtaining localscale information at the initial sampling round, the local scaleinformation may be added to information to be stratified through variousapproaches including choosing the highest locally correlated covariates,updating the regional model and/or constructing local predictions, andpostulating likely sequestration rates as per land use.

Selecting Locations for Determining Sample Carbon Content

A sample (with replacement) may be randomly drawn or selected at aminimum of one sampling point, and, in one such embodiment, a minimum oftwo sampling points (i.e., locations or composites) from within eachstratum. Extra sampling points may also be drawn as backups for fielddecisions relating to issues such as lack of access and inappropriatelocations such as dams, trees or roads that are below the practicalresolution of the land use classification. Drawing sample points asclose to spatially random as is practical requires creation of a finerspatial resolution of each stratum, which can be roughly equivalent tothe positional accuracy of commonly available GPS equipment (i.e., 30 mresolution re-sampled to 5 m resolution before selection of randomsample from each stratum).

Sample points are typically allocated equally between strata with theminimum quantity or number of sampling points informed by the needfor >2 composites per stratum. Beyond this level, additional samplepoints are usually informed by the level of investment available andoptimal levels will vary with landscape and land use. As a general rule,the quantity or number of sampling points within each stratum isdetermined or designated as one, and, in one such embodiment, two,greater than the total quantity or number of strata. For instance, asample of 48 sampling points for 6 strata, with 8 sampling points perstratum, may be selected.

Once the total quantity or number of sampling units has been decided andequally allocated between strata, actual sampling points are selectedusing random sampling with replacement. At this point, a regular grid ofspatial coordinates to a 5 m resolution is used as the basis to selectpoints, as this is comparable to the error of common handheld GPS unitswhilst still yielding a reasonable sized dataset to enable greater easeof processing (i.e., a 1 m resolution grid contains 25 times theinformation than that of a 5 m resolution grid). The prediction functionfor soil carbon for instance, can only have a resolution as fine as itsfinest predictor (in this instance the 30 m elevation model).

FIG. 3 (right) depicts 8 randomly selected locations (with replacement)within each stratum. Soil samples are collected to maximum practicalsampling depth (nominally 1 m) from within each stratum. The cuttingshoe diameter (for determining the core area), push depth, pulled corelength and hole depth (after extraction) are recorded forcompression/expansion corrections if carbon density (as opposed to massper area) reporting is desired.

Whole core soil samples may be physically composited within strata toreduce analysis costs. If soil samples are to be composited, the bulkingprocess may occur within strata and yield a minimum of 2 composites,with individual air dry weight and volume recorded prior to mixing orkept separate to provide in situ information for refinement of SOCprediction and stratification for the next soil carbon quantificationprocess. Additionally, the process of bulking, whether for a mass or aspatial coordinate system, may require that the bulked units arenominally equal in layer thickness or mass. For example, a composite maybe formed by bulking a 20 cm layer of one core soil sample with a 20 cmlayer of another core soil sample from the same stratum. As anotherexample, a composite may be formed by bulking 200 g of soil from onecore soil sample with 200 g of soil from another core soil sample fromthe same stratum. The cores may be randomly matched.

As auditing rounds progress it is expected that compositing will becomethe default practice due to decreasing gains in re-stratification andthe economical gains of fewer analyses. However re-stratificationrequires careful consideration of the chosen reporting form (carbondensity or mass per unit area (to standard mass) and recording of therequired individual core variables). Significant changes in land usewill likely require re-stratification (through processing separatesamples) to reflect altered landscape patterns and adjustments of thenew system before switching back to compositing.

Determining Sample and Total Carbon Content

Soil samples (whether composited, individual or sub-individual) areassessed for sample carbon content utilizing standard combustionmethodologies to determine the total carbon content in the unit of land.The sample carbon content may be determined using a 53 μm Vario Max CNSanalyzer, which may measure carbon content by combustion of the soilsamples, or using near infrared spectroscopy analysis of the soilsamples in the field. The measurement of content carbon may involvecorrection for inorganic carbon so that organic carbon content may bedetermined. The measured sample carbon content may be reported byabsolute, percentage or fractional weight or mass of carbon, and mayinclude any carbon compounds such as elemental carbon, carbon oxides andcarbonates.

There are two coordinate systems for reporting total carbon content: (1)the mass or material coordinate system, and (2) the volumetric orspatial coordinate system. The mass or material coordinate systemreports total carbon content in a predetermined or standard mass of soilper unit area (e.g., 1500 kg m⁻² of air dry soil) of the unit of land,whereas the volumetric or space coordinate system reports total carboncontent in a predetermined or standard soil depth (e.g., 100 cm) perunit area of the unit of land.

The volumetric or spatial coordinate system is considered lessadvantageous due to greater variability introduced via densitydetermination (i.e., sampling consistently to 1 m depth whilst avoidingcompression or expansion and assuming consistent bulk density of soil inspace is highly improbable). Therefore changes in soil carbon may beascribed to any change in concentration, but also to a greater sampledmass with a given volume for instance.

The advantages of the mass or material coordinate system over thevolumetric or spatial coordinate systems include:

-   -   seasonal or management effects on bulk density do not confound        changes in SOC storage which increases accuracy of estimates;    -   a set standard reporting mass allows greater precision in        determining changes in SOC storage between discrete auditing        events; and    -   monitoring of SOC is simpler, requiring fewer corrections and        therefore reduced uncertainties.

In the instance of insufficient soil depth to obtain sufficient materialmass to reach the predetermined mass or depth, any additional mass/depthadded in the calculation process may be assumed to contain no additionalcarbon.

Examples of Total Carbon Content Calculation

For illustration purposes, examples are given below for the calculationof total carbon content using the two coordinate systems. In addition,two sub-variants of each coordinate system, constituted by a sample withand without the use of composites, are also presented.

A reduced dataset has been used for these example calculations. Thereduced dataset consists of hypothetical soil sample results from 2strata, each having 3 cores (i.e., selected locations or samplingpoints). Each core is divided into three layers of soil and variousobservations (including layer mass and depth) at each layer are made. Asummary of the variables used in these examples is provided in FIG. 4 .A more detailed description of the statistical theory applied in theseexamples is also provided in Appendix A.

EXAMPLE 1 Mass Coordinate System—Single Cores with No Composites

The mass or material coordinate approach, utilizing a standard orpredetermined mass per unit area of 1500 kg·m⁻² of oven-dry mass with nocompositing is presented here for the sample dataset.

FIG. 5A shows the sample carbon content at one of the selected locations(with core ID “2 i”) of each of the three layers as well as processeddata including cumulative carbon (C) mass as a function of cumulativeoven-dry (OD) soil mass for a single core as described in Eqs. 1.1-1.7.

$\begin{matrix}{{{AD}_{mass} - G_{w}} = {AD}_{soil}} & (1.1) \\{{{AD}_{soil} - \left( {{AD}_{soil} \times \theta} \right)} = {OD}_{soil}} & (1.2) \\{{\left( \frac{\left( {{OD}_{soil} + G_{w}} \right)}{\left( {\pi \times C_{r}^{2}} \right)} \right) \times \frac{10000}{1000}} = {OD}_{mass}} & (1.3) \\{{\left( \frac{{OD}_{soil}}{\left( {\pi \times C_{r}^{2}} \right)} \right) \times \frac{10000}{1000}} = {OD}_{soil}} & (1.4) \\{{\left( \frac{{OD}_{soil}}{100} \right) \times C\mspace{14mu}\%} = C_{mass}} & (1.5) \\{{\sum\limits_{l = 1}^{i}{OD}_{{mass}_{l}}} = {OD}_{{mass}_{i}}} & (1.6) \\{{\sum\limits_{l = 1}^{i}C_{{mass}_{l}}} = C_{{mass}_{i}}} & (1.7)\end{matrix}$

FIG. 5B depicts a linear fit interpolation to obtain C mass to thepredetermined or standard mass per unit area as described in Eq. 1.8.Approaches such as spline fitting may also be used at this stage butthis requires a minimum of 3 observations with mass. In this example,the sample carbon content is determined to be 9.42 kg m⁻².

$\begin{matrix}{{OD}_{STmass} = {{OD}_{{mass}\; 1} + {\left( {C_{STmass} - C_{{mass}\; 1}} \right)\frac{\left( {{OD}_{{mass}\; 2} - {OD}_{{mass}\; 1}} \right)}{\left( {C_{{mass}\; 2} - C_{{mass}\; 1}} \right)}}}} & (1.8)\end{matrix}$

In some instances where insufficient soil mass is recovered, thepreference is not to use an extrapolation method but to take the maximumC mass obtained and assume any additional mass to reach the standardcontains no additional carbon.

Eqs. 1.9 to 1.13 and FIG. 5C illustrate the determination of average ormean sample carbon content, its variance and standard error (normalizedto the predetermined or standard mass) across the three selectedlocations in each stratum (core ID's 1 e, 1 f and 1 g in Stratum 1 andcore ID's 2 k, 2 a and 2 i in Stratum 2).

$\begin{matrix}{\mspace{79mu}{{\left( \frac{1}{\left( {v \times n} \right)} \right) \times \left( {\sum\limits_{k = 1}^{m}C_{{STmass}_{k}}} \right)} = C_{St}}} & (1.9) \\{{\left( \frac{1}{\left( {n - 1} \right){nv}^{2}} \right) \times \left\{ {{\sum\limits_{k = 1}^{m}\frac{C_{{STmass}_{k}}^{2}}{n_{k}}} - {\frac{1}{n}\left( {\sum\limits_{k = 1}^{m}C_{{STmass}_{k}}} \right)^{2}}} \right\}} = {V\left( C_{St} \right)}} & (1.10) \\{\mspace{79mu}{\sqrt{V\left( C_{St} \right)} = {S\left( C_{St} \right)}}} & (1.11) \\{\mspace{79mu}{\frac{\left( {C_{St} \times {St}_{a}} \right)}{1000} = C_{content}}} & (1.12) \\{\mspace{79mu}{{{V\left( C_{St} \right)} \times {St}_{a}^{2}} = {V\left( C_{content} \right)}}} & (1.13)\end{matrix}$

Eqs. 1.15 to 1.20 and FIG. 5D illustrate the determination of combiningsample carbon content from all strata to determine the total carboncontent (including the average, variance, standard error, confidenceintervals, such as a 95% confidence interval, and minimum detectabledifference) in the unit of land.

$\begin{matrix}{{\sum\limits_{i = 1}^{St}C_{{content}_{i}}} = {FC}_{content}} & (1.14) \\{\frac{\sum\limits_{i = 1}^{St}{V\left( C_{content} \right)}_{i}}{1000000} = {V\left( {FC}_{content} \right)}} & (1.15) \\{\sqrt{V\left( {FC}_{content} \right)} = {S\left( {FC}_{content} \right)}} & (1.16) \\{{{FC}_{content} \pm {t_{0.95}\sqrt{V\left( {FC}_{content} \right)}}} = {{\pm 95}\%\mspace{14mu}{C.I.}}} & (1.17) \\{{\sqrt{2} \times \left( \frac{{\pm 95}\%\mspace{14mu}{C.I}}{\left( \frac{{FC}_{content}}{100} \right)} \right)} = {{mdd}\;\Delta\mspace{14mu}\%\mspace{14mu}{FC}_{content}}} & (1.18) \\{{\left( \frac{{FC}_{content}}{100} \right) \times \Delta\mspace{14mu}\%\mspace{14mu}{FC}_{content}} = {{mdd}\;\Delta\;{FC}_{content}}} & (1.19) \\{\frac{\left( \frac{{mdd}\;\Delta\;{FC}_{content}}{1000} \right)}{\left( {\sum\limits_{i = 1}^{k}{St}_{a_{i}}} \right)} = {{mdd}\;\Delta\;{FC}_{storage}}} & (1.20)\end{matrix}$

Eqs. 1.21 to 1.24 define the change in total carbon content (includingthe average, variance, standard error, confidence intervals, such as a95% confidence interval) between time t₁ and time t₂.FC _(content) _(t1) −FC _(content) _(t2) =ΔFC _(storage)  (1.21)V(FC _(content) _(t1) )+V(FC _(content) _(t2) )−2ρ√{square root over(V(FC _(content) _(t1) ))}√{square root over (V(FC _(content) _(t2)))}=V(ΔFC _(storage))   (1.22)√{square root over (V(ΔFC _(storage)))}=S(ΔFC _(storage))  (1.23)FC _(content) ±t _(0.95)√{square root over (V(FC _(content)))}=±95%C.I.  (1.24)

EXAMPLE 2 Mass Coordinate System—with Composites

The mass or material coordinate approach, utilizing a predetermined orstandard mass of 1500 kg·m⁻² of oven-dry mass with compositing ispresented here for the sample dataset. Composites within this methodrequire bulking of equal amounts of OD soil mass per layer. Properrandomization of composited layers (or cores) is required for thisapproach as estimates of average total carbon content and its variance(in particular) can be manipulated either deliberately or throughunintended preference (i.e., combining similar textured or coloredcores). This can be seen by comparing summary results in FIG. 5D andFIG. 6C.

FIG. 6A shows the sample carbon content of a composite of two cores(with core ID's “2 a” and “2 i”) of each of the three layers as well asprocessed data including cumulative carbon (C) mass as a function ofcumulative oven-dry (OD) soil mass for a composite of two cores and isdescribed in Eqs. 2.1-2.7

$\begin{matrix}{{{AD}_{mass} - G_{w}} = {AD}_{soil}} & (2.1) \\{{{AD}_{soil} - \left( {{AD}_{soil} \times \theta} \right)} = {OD}_{soil}} & (2.2) \\{{\left( \frac{\left( {{OD}_{soil} + G_{w}} \right)}{\left( {\pi \times C_{r}^{2}} \right) \times v} \right) \times \frac{10000}{1000}} = {OD}_{mass}} & (2.3) \\{{\left( \frac{{OD}_{soil}}{\left( {\pi \times C_{r}^{2}} \right)} \right) \times \frac{10000}{1000}} = {OD}_{soil}} & (2.4) \\{{\left( \frac{{OD}_{soil}}{100} \right) \times C\mspace{14mu}\%} = C_{mass}} & (2.5) \\{{\sum\limits_{l = 1}^{i}{OD}_{{mass}_{l}}} = {OD}_{{mass}_{i}}} & (2.6) \\{{\sum\limits_{l = 1}^{i}C_{{mass}_{l}}} = C_{{mass}_{i}}} & (2.7)\end{matrix}$

FIG. 6B and Eq. 2.8 illustrate a linear fit interpolation to obtain Cmass to the standard mass. Approaches such as spline fitting may also beused at this stage but this requires a minimum of 3 observations withmass. In certain instances where insufficient soil mass is recovered,the preference is not to use an extrapolation method but to take themaximum C mass obtained and assume any additional mass to reach thestandard contains no additional carbon. In this example, the samplecarbon content of the composite is determined to be 10.22 kg m⁻².

$\begin{matrix}{{OD}_{STmass} = {{OD}_{{mass}\; 1} + {\left( {C_{STmass} - C_{{mass}\; 1}} \right)\frac{\left( {{OD}_{{mass}\; 2} - {OD}_{{mass}\; 1}} \right)}{\left( {C_{{mass}\; 2} - C_{{mass}\; 1}} \right)}}}} & (2.8)\end{matrix}$

Eqs. 2.9 to 2.13 and FIG. 6C illustrate the determination of averagecarbon content, variance and standard error (to the predetermined orstandard mass) across the three selected locations in each stratum (coreID's 1 e, 1 f and 1 g in Stratum 1 and core ID's 2 k, 2 a and 2 i inStratum 2).

$\begin{matrix}{\mspace{79mu}{{C_{STmass} \times k} = C_{{STmass}_{k}}}} & (2.9) \\{\mspace{79mu}{{\left( \frac{1}{({nv})} \right) \times \left( {\sum\limits_{k = 1}^{m}C_{{STmass}_{k}}} \right)} = C_{St}}} & (2.10) \\{{\left( \frac{1}{\left( {m - 1} \right){nv}^{2}} \right) \times \left\{ {{\sum\limits_{k = 1}^{m}\frac{C_{{STmass}_{k}}^{2}}{n_{k}}} - {\frac{1}{n}\left( {\sum\limits_{k = 1}^{m}C_{{STmass}_{k}}} \right)^{2}}} \right\}} = {V\left( C_{St} \right)}} & (2.11) \\{\mspace{79mu}{\sqrt{V\left( C_{St} \right)} = {S\left( C_{St} \right)}}} & (2.12) \\{\mspace{79mu}{\frac{\left( {C_{St} \times {St}_{a}} \right)}{1000} = C_{content}}} & (2.13) \\{\mspace{79mu}{{{V\left( C_{St} \right)} \times {St}_{a}^{2}} = {V\left( C_{content} \right)}}} & (2.14)\end{matrix}$

Eqs. 2.15 to 2.21 and FIG. 6D illustrate the process of combining samplecarbon content to obtain total carbon content (including variance,standard error, a confidence interval such as a 95% confidence interval)in the unit of land.

$\begin{matrix}{{\sum\limits_{i = 1}^{St}C_{{content}_{i}}} = {FC}_{content}} & (2.15) \\{\frac{\sum\limits_{i = 1}^{St}{V\left( C_{content} \right)}_{i}}{1000000} = {V\left( {FC}_{content} \right)}} & (2.16) \\{\sqrt{V\left( {FC}_{content} \right)} = {S\left( {FC}_{content} \right)}} & (2.17) \\{{{FC}_{content} \pm {t_{0.95}\sqrt{V\left( {FC}_{{content}\;} \right)}}} = {{\pm 95}\%\mspace{14mu}{C.I.}}} & (2.18) \\{{\sqrt{2} \times \left( \frac{{\pm 95}\%\mspace{14mu}{C.I}}{\left( \frac{{FC}_{content}}{100} \right)} \right)} = {\Delta\mspace{14mu}\%\mspace{14mu}{FC}_{content}}} & (2.19) \\{{\left( \frac{{FC}_{content}}{100} \right) \times \Delta\mspace{14mu}\%\mspace{14mu}{FC}_{content}} = {\Delta\;{FC}_{content}}} & (2.20) \\{\frac{\left( \frac{{mdd}\;\Delta\;{FC}_{content}}{1000} \right)}{\left( {\sum\limits_{i = 1}^{k}{St}_{a_{i}}} \right)} = {{mdd}\;\Delta\;{FC}_{storage}}} & (2.21)\end{matrix}$

Eqs. 2.22 to 2.25 define the change in total carbon content (includingthe average, variance, standard error, confidence intervals, such as a95% confidence interval) between time t₁ and time t₂.FC _(content) _(t1) −FC _(content) _(t2) =ΔFC _(storage)  (2.22)V(FC _(content) _(t1) )+V(FC _(content) _(t2) )−2ρ√{square root over(V(FC _(content) _(t1) ))}√{square root over (V(FC _(content) _(t2)))}=V(ΔFC _(storage))   (2.23)√{square root over (V(ΔFC _(storage)))}=S(ΔFC _(storage))  (2.24)FC _(content) ±t _(0.95)√{square root over (V(FC _(content)))}=±95%C.I.  (2.25)

EXAMPLE 3 Spatial Coordinate Approach—Single Cores No Composites

The volumetric or spatial coordinate approach, utilizing a standard orpredetermined soil depth of 100 cm without compositing is presented herefor the sample dataset.

FIG. 7A shows the sample carbon content at one of the selected locations(with core ID “2 i”) of each of the three layers as well as processeddata including cumulative carbon (C) density as a function of depth fora single core is described in Eqs. 3.1-3.9.

$\begin{matrix}{{{AD}_{mass} - G_{w}} = {AD}_{soil}} & (3.1) \\{{{AD}_{soil} - \left( {{AD}_{soil} \times \theta} \right)} = {OD}_{soil}} & (3.2) \\{{\left( {\pi \times C_{r}^{2}} \right) \times L_{l}} = L_{v}} & (3.3) \\{\frac{G_{w}}{2.65} = G_{v}} & (3.4) \\{{L_{v} - G_{v}} = {SP}_{v}} & (3.5) \\{\frac{{OD}_{soil}}{{SP}_{v}} = {SP}_{BD}} & (3.6) \\{{\left( \frac{C\mspace{14mu}\%}{100} \right) \times {SP}_{BD}} = C_{dens}} & (3.7) \\{{\left( \frac{\left( {C_{dens} \times 10000} \right)}{1000} \right) \times L_{l}} = C_{{dens}_{l}}} & (3.8) \\{{\sum\limits_{i = 1}^{l}C_{{dens}_{l}}} = C_{{dens}_{i}}} & (3.9)\end{matrix}$

FIG. 7B depicts a linear fit approach to interpolation to obtain Cdensity to the predetermined or standard depth as described in Eq. 3.10.Approaches such as spline fitting may also be used at this stage butthis requires a minimum of 3 observations with depth. In certaininstances where insufficient depth is recovered, the preference is notto use an extrapolation method but to take the maximum C densityobtained and assume any additional depth to reach the standard depthcontains no additional carbon.

$\begin{matrix}{L_{ST} = {L_{l\; 1} + {\left( {C_{STdens} - C_{{dens}\; 1}} \right)\frac{\left( {L_{l\; 2} - L_{l\; 1}} \right)}{\left( {C_{{dens}\; 2} - C_{{dens}\; 1}} \right)}}}} & (3.10)\end{matrix}$

Eq. 3.11 to 3.15 and FIG. 7C illustrate the determination of averagecarbon content, variance and standard error (to the standard depth)across the three selected locations in each stratum (core ID's 1 e, 1 fand 1 g in Stratum 1 and core ID's 2 k, 2 a and 2 i in Stratum 2).

$\begin{matrix}{\mspace{79mu}{{\left( \frac{1}{\left( {v \times n} \right)} \right) \times \left( {\sum\limits_{k = 1}^{m}C_{{STdens}_{k}}} \right)} = C_{St}}} & (3.11) \\{{\left( \frac{1}{\left( {n - 1} \right){nv}^{2}} \right) \times \left\{ {{\sum\limits_{k = 1}^{m}\frac{C_{{STdens}_{k}}^{2}}{n_{k}}} - {\frac{1}{n}\left( {\sum\limits_{k = 1}^{m}C_{{STdens}_{k}}} \right)^{2}}} \right\}} = {V\left( C_{St} \right)}} & (3.12) \\{\mspace{79mu}{\sqrt{V\left( C_{St} \right)} = {S\left( C_{St} \right)}}} & (3.13) \\{\mspace{79mu}{\frac{\left( {C_{St} \times {St}_{a}} \right)}{1000} = C_{content}}} & (3.14) \\{\mspace{79mu}{{{V\left( C_{St} \right)} \times {St}_{a}^{2}} = {V\left( C_{content} \right)}}} & (3.15)\end{matrix}$

Eq. 3.16 to 3.22 and FIG. 7D illustrate the combining of the samplecarbon content from all strata to determine the total carbon content(including the average, variance, standard error, confidence intervals,such as a 95% confidence interval, and minimum detectable difference) inthe unit of land.

$\begin{matrix}{{\sum\limits_{i = 1}^{St}C_{{content}_{i}}} = {FC}_{content}} & (3.16) \\{\frac{\sum\limits_{i = 1}^{St}{V\left( C_{content} \right)}_{i}}{1000000} = {V\left( {FC}_{content} \right)}} & (3.17) \\{\sqrt{V\left( {FC}_{content} \right)} = {S\left( {FC}_{content} \right)}} & (3.18) \\{{{FC}_{content} \pm {t_{0.95}\sqrt{V\left( {FC}_{content} \right)}}} = {{\pm 95}\%\mspace{14mu}{C.I.}}} & (3.19) \\{{\sqrt{2} \times \left( \frac{{\pm 95}\%\mspace{14mu}{C.I}}{\left( \frac{{FC}_{content}}{100} \right)} \right)} = {\Delta\mspace{14mu}\%\mspace{14mu}{FC}_{content}}} & (3.20) \\{{\left( \frac{{FC}_{content}}{100} \right) \times \Delta\mspace{14mu}\%\mspace{14mu}{FC}_{content}} = {\Delta\;{FC}_{content}}} & (3.21) \\{\frac{\left( \frac{{mdd}\;\Delta\;{FC}_{content}}{1000} \right)}{\left( {\sum\limits_{i = 1}^{St}{St}_{a_{i}}} \right)} = {{mdd}\;\Delta\;{FC}_{storage}}} & (3.22)\end{matrix}$

Eqs. 3.23 to 3.26 define the change in total carbon content (includingthe average, variance, standard error, confidence intervals, such as a95% confidence interval between time t₁ and time t₂.FC _(content) _(t1) −FC _(content) _(t2) =ΔFC _(storage)  (3.23)V(FC _(content) _(t1) )+V(FC _(content) _(t2) )−2ρ√{square root over(V(FC _(content) _(t1) ))}√{square root over (V(FC _(content) _(t2)))}=V(ΔFC _(storage))   (3.24)√{square root over (V(ΔFC _(storage)))}=S(ΔFC _(storage))  (3.25)FC _(content) ±t _(0.95)√{square root over (V(FC _(content)))}=±95%C.I.  (3.26)

EXAMPLE 4 Spatial Coordinate Approach—with Composites

The volumetric or spatial coordinate approach, utilizing a predeterminedor standard depth of 100 cm with compositing is presented here for thesample dataset.

FIG. 8A shows the sample carbon content of a composite of two cores(with core ID's “2 a” and “2 i”) as well as processed data includingcumulative carbon (C) density as a function of depth for a composite oftwo cores and is described in Eqs. 4.1 to 4.8.

$\begin{matrix}{{{AD}_{mass} - G_{w}} = {AD}_{soil}} & (4.1) \\{{{AD}_{soil} - \left( {{AD}_{soil} \times \theta} \right)} = {OD}_{soil}} & (4.2) \\{{\left( {\pi \times C_{r}^{2}} \right) \times k \times L_{l}} = L_{v}} & (4.3) \\{\frac{G_{w}}{2.65} = G_{v}} & (4.4) \\{{L_{v} - G_{v}} = {SP}_{v}} & (4.5) \\{\frac{{OD}_{soil}}{{SP}_{v}} = {SP}_{BD}} & (4.6) \\{{\left( \frac{C\mspace{14mu}\%}{100} \right) \times {SP}_{BD}} = C_{dens}} & (4.7) \\{{\left( \frac{\left( {C_{dens} \times 10000} \right)}{1000} \right) \times L_{l}} = C_{{dens}_{l}}} & (4.8)\end{matrix}$

Eq. 4.9 describes a linear fit o interpolation to obtain C density tothe standard depth:

$\begin{matrix}{{\left( \frac{C_{{dens}_{l}}}{L_{l}} \right) \times 100} = C_{STdens}} & (4.9)\end{matrix}$

Eqs. 4.10 to 4.14 and FIG. 8B illustrate the determination of theaverage carbon content, variance and standard error (to thepredetermined or standard depth) across the three selected locations ineach stratum (core ID's 1 e, 1 f and 1 g in Stratum 1 and core ID's 2 k,2 a and 2 i in Stratum 2).

$\begin{matrix}{\mspace{79mu}{{\left( \frac{1}{\left( {v \times n} \right)} \right) \times \left( {\sum\limits_{k = 1}^{m}C_{{STdens}_{k}}} \right)} = C_{St}}} & (4.10) \\{{\left( \frac{1}{\left( {n - 1} \right){nv}^{2}} \right) \times \left\{ {{\sum\limits_{k = 1}^{m}\frac{C_{{STdens}_{k}}^{2}}{n_{k}}} - {\frac{1}{2}\left( {\sum\limits_{k = 1}^{m}C_{{STdens}_{k}}} \right)^{2}}} \right\}} = {V\left( C_{St} \right)}} & (4.11) \\{\mspace{79mu}{\sqrt{V\left( C_{St} \right)} = {S\left( C_{St} \right)}}} & (4.12) \\{\mspace{79mu}{\frac{\left( {C_{St} \times {St}_{a}} \right)}{1000} = C_{content}}} & (4.13) \\{\mspace{79mu}{{{V\left( C_{St} \right)} \times {St}_{a}^{2}} = {V\left( C_{content} \right)}}} & (4.14)\end{matrix}$

Eqs. 4.15 to 4.21 and FIG. 8C illustrate the process of combining samplecarbon content to obtain total carbon content (including variance,standard error, a confidence interval such as a 95% confidence intervalas well as minimum detectable difference) in the unit of land.

$\begin{matrix}{{\sum\limits_{i = 1}^{St}C_{{content}_{i}}} = {FC}_{content}} & (4.15) \\{\frac{\sum\limits_{i = 1}^{St}{V\left( C_{content} \right)}_{i}}{1000000} = {V\left( {FC}_{content} \right)}} & (4.16) \\{\sqrt{V\left( {FC}_{content} \right)} = {S\left( {FC}_{content} \right)}} & (4.17) \\{{{FC}_{content} \pm {t_{0.95}\sqrt{V\left( {FC}_{content} \right)}}} = {{\pm 95}\%\mspace{14mu}{C.I.}}} & (4.18) \\{{\sqrt{2} \times \left( \frac{{\pm 95}\%\mspace{14mu}{C.I}}{\left( \frac{{FC}_{content}}{100} \right)} \right)} = {\Delta\mspace{14mu}\%\mspace{14mu}{FC}_{content}}} & (4.19) \\{{\left( \frac{{FC}_{content}}{100} \right) \times \Delta\mspace{14mu}\%\mspace{14mu}{FC}_{content}} = {\Delta\;{FC}_{content}}} & (4.20) \\{\frac{\left( \frac{{mdd}\;\Delta\;{FC}_{content}}{1000} \right)}{\left( {\sum\limits_{i = 1}^{k}{St}_{a_{i}}} \right)} = {{mdd}\;\Delta\;{FC}_{storage}}} & (4.21)\end{matrix}$

Eq. 4.22 to 4.25 define the change in total carbon content (includingthe average, variance, standard error, confidence intervals, such as a95% confidence interval, and minimum detectable difference) between timet₁ and time t₂.FC _(content) _(t1) −FC _(content) _(t2) =ΔFC _(storage)  (4.22)V(FC _(content) _(t1) )+V(FC _(content) _(t2) )−2ρ√{square root over(V(FC _(content) _(t1) ))}√{square root over (V(FC _(content) _(t2)))}=V(ΔFC _(storage))   (4.23)√{square root over (V(ΔFC _(storage)))}=S(ΔFC _(storage))  (4.24)FC _(content) ±t _(0.95)√{square root over (V(FC _(content)))}=±95%C.I.  (4.25)

Having described several embodiments of the method according to thepresent disclosure, it should be apparent that the disclosure has thefollowing advantages:

-   -   “System gaming” such as manipulation of soil carbon        quantification results by, for example, deliberate carbon        sequestration at known sampling locations is avoided by        selecting sampling points with randomness.    -   A confidence interval (or other statistical measures such as        variance) of the soil carbon may be determined so that the        uncertainty in the soil carbon quantification results may be        specified.    -   When reporting soil carbon using the mass coordinate system        (i.e., using a predetermined or standard mass of soil per unit        area), the compactness of the soil does not affect the soil        carbon quantification results.    -   The method does not impede nor prescribe nor penalise changes in        land use; does not impede ‘real’ reductions in fossil carbon        emissions (due to temporary crediting for SOC).    -   The method reduces risk to the landholder for maintaining        sequestration over indefinite periods.    -   The method provides an ongoing (and validated) revenue stream        for landholders increasing the likelihood of SOC perpetuation.    -   Verification of a carbon sequestration contract for sequestered        carbon can be verified for the period of time over which        auditing takes place.

It will be appreciated by persons skilled in the art that numerousvariations and/or modifications may be made to the disclosure as shownin the specific embodiments without departing from the spirit or scopeof the disclosure as broadly described. For example, the total carboncontent may be reported or normalized to a soil mass or depth other than1500 kg m⁻² or 100 cm. The present embodiments are, therefore, to beconsidered in all respects as illustrative and not restrictive.

Appendix A: Theory

The estimation of SOC storage and uncertainties is inferred utilizingWeighted Least Squares regression as follows. Assume that n cores weretaken from the stratum, which were used to make m composites (m>1). Letn_(k) be the quantity or number of cores in composite k, making a volumeof x_(k) m³, with a measured carbon content of c_(k) kg. The volume of acomposite equals its quantity or number of cores times the standard corevolume (v): x_(k)=n_(k)·V.

The mean carbon density of stratum j is estimated by Weighted LeastSquares regression, with equation: c=X·β+e, where

c=[c₁ . . . c_(k) . . . c_(m)]′: the vector of carbon contents,

X=[x₁ . . . x_(k) . . . x_(n)]′: the m×1 design-matrix with compositevolumes, β: the mean carbon density of the stratum, e: the vector ofrandom errors.

WLS estimate of β: {circumflex over (β)}=(X′V⁻¹X)⁻¹X′V⁻¹c where V⁻¹ isthe diagonal matrix of weights, with 1/n₁, . . . , 1/n_(m) on thediagonal, because the sampling variance of the carbon content of acomposite is proportional to the quantity or number of cores.

The formula can be simplified using

X^(′)V⁻¹ = [1  …  1]v X^(′)V⁻¹X = nv²${X^{\prime}V^{- 1}c} = {v{\sum\limits_{k = 1}^{m}c_{k}}}$which leads to:

${\hat{\beta} = {\frac{1}{nv}{\sum\limits_{k = 1}^{m}c_{k}}}},$(i.e., the total carbon content divided by the total volume of thecomposites).

The variance of β is more complicated. This can be estimated by:

${\hat{V}\left( \hat{\beta} \right)} = {{\frac{1}{m - 1} \cdot c^{\prime}}V^{- 1}\left\{ {I - {{X\left( {X^{\prime}V^{- 1}X} \right)}^{- 1}X^{\prime}V^{- 1}}} \right\}{c\left( {X^{\prime}V^{- 1}X} \right)}^{- 1}}$which simplifies to:

${\hat{V}\left( \hat{\beta} \right)} = {\frac{1}{\left( {m - 1} \right){nv}^{2}} \cdot \left\{ {{\sum\limits_{k = 1}^{m}\frac{c_{k}^{2}}{n_{k}}} - {\frac{1}{n}\left( {\sum\limits_{k = 1}^{m}c_{k}} \right)^{2}}} \right\}}$The variance estimates thus obtained for each of the strata can beimputed in

${\hat{V}\left( {SOC}_{farm} \right)} = {\sum\limits_{h = 1}^{H}{a_{h}^{2}{\hat{V}\left( {\hat{\beta}}_{h} \right)}}}$Where SOC_(farm) is the total SOC storage on the farm, H is the quantityor number of strata, a_(h) ² is the relative area squared of eachstratum.

The standard error of the estimated mean:{circumflex over (S)}(SOC_(farm))=√{square root over ({circumflex over(V)}(SOC_(farm)))}Confidence intervals for SOC storage:

${SOC}_{farm} \pm {t_{1 - \frac{\alpha}{2}} \cdot \sqrt{\hat{V}\left( {SOC}_{farm} \right)}}$Simple Numerical Example for 2 Composites and 1 Stratum Utilizing aVolumetric Approach

Given sample data:

n=3

v=0.01 m³

m=2

V=[1, 2]′

X=[0.01, 0.02]′ m³

c=[0.2, 0.5]′kg

Estimates:

$\mspace{79mu}{\hat{\beta} = {{\frac{1}{3 \times 0.01}\left( {0.2 + 0.5} \right)} = {23.33\mspace{14mu}{{kg} \cdot m^{- 3}}}}}$${\hat{V}\left( \hat{\beta} \right)} = {{\frac{1}{2 \times 3 \times 0.01^{2}}\left\{ {\frac{0.2^{2}}{1} + \frac{0.5^{2}}{2} - {\frac{1}{3}\left( {0.2 + 0.5} \right)^{2}}} \right\}} = {2.77\mspace{14mu}{{kg}^{2} \cdot m^{- 6}}}}$$\mspace{79mu}{{\hat{S}\left( \hat{\beta} \right)} = {\sqrt{\hat{V}\left( \hat{\beta} \right)} = {1.66\mspace{14mu}{{kg} \cdot m^{- 3}}}}}$SOC Storage Through Time

After the initial baseline audit, follow up audits are conducted atspecified intervals (at roughly the same position in the annual cycle)and serve to monitor changes in SOC storage. Each successive audit mayutilize the previous stratification or a newly constructedstratification, may vary the quantity or number of strata and sampleunits from each as long as each sample draw is random within eachstratum and the minimum requirements of the methodology are met. Drawingsamples from different points between time 1 and time 2 allows samplingto be independent and also reduces the likelihood of system gaming—asignificant weakness of static sampling points.

A time-weighted measure of SOC storage:

${SOC}_{sequestered} = \frac{{SOC}_{farm}^{t\; 2} - {SOC}_{farm}^{t\; 1}}{t_{2} - t_{1}}$Variance between time 1 & time 2 given independent sampling:V(SOC_(farm) ^(t2))+V(SOC_(farm) ^(t1))=V(SOC_(sequestered))

Additionally, given that sampling is independent it can be assumed thatthe variance of time 1 should be equal to that of time 2, allowing theestimation of the minimum detectable difference in SOC from time 1 whichcan be used to inform a suitable interval period between monitoringevents (i.e., if the estimate at time 1 has a large variance then theminimum detectable difference in SOC will also be larger—implying that alonger period between monitoring events would be more cost-effective).

The invention claimed is:
 1. A method of quantifying soil carbon in aunit of land, the method comprising: (a) obtaining an estimated spatialdistribution of soil carbon content in the unit of land by: (i)correlating information associated with the unit of land with soilcarbon distribution, and (ii) inputting the correlated information intoa soil carbon content prediction model to predict the estimated spatialdistribution of soil carbon content; and (b) thereafter, independentlyauditing the obtained estimated spatial distribution of soil carboncontent in the unit of land by: (i) stratifying, at least partiallybased on at least one of: a diversity of the unit of land, a land usetype, and a total area of the unit of land, the unit of land into atotal quantity of at least two strata, wherein the stratificationincludes determining one or more stratum boundaries between the totalquantity of at least two strata, the determination of the one or morestratum boundaries includes determining one or more optimum stratumboundaries under Neyman allocation, and the total quantity of at leasttwo strata is based, at least partly, on the obtained estimated spatialdistribution of soil carbon content; (ii) after stratifying the unit ofland into the total quantity of at least two strata: (1) determining aquantity of locations to sample within each strata, the quantity oflocations to sample within each strata being at least one more than thetotal quantity of at least two strata and being based, at least partly,on the obtained estimated spatial distribution of soil carbon content,and (2) reducing sampling variance and fraudulent manipulation of soilcarbon quantification results by randomly selecting, from each strata ofthe total quantity of at least two strata, the quantity of locationsfrom that strata; (iii) using at least one of a CNS analyser and a nearinfrared spectroscopic analyser to determine sample soil carbon contentassociated with the selected quantity of locations; and (iv) determiningtotal soil carbon content in the unit of land based, at least partly, onthe sample soil carbon content.
 2. The method of claim 1, whereinobtaining the estimated spatial distribution of soil carbon contentincludes obtaining a regional prediction of spatial distribution of soilcarbon content.
 3. The method of claim 1, which includes downscaling theinformation associated with the unit of land.
 4. The method of claim 1,wherein determining the sample soil carbon content includes measuringthe sample soil carbon content as measured sample soil carbon content.5. The method of claim 1, wherein determining the sample soil carboncontent includes determining the sample soil carbon content in one ormore layers of measured mass of soil over a determined area of the unitof land.
 6. The method of claim 5, wherein determining the sample soilcarbon content includes determining any one or more of: a cutting shoediameter, a push depth, a pulled core length and a hole depth,associated with the measured mass of soil.
 7. The method of claim 1,wherein determining the sample soil carbon content includes determiningcomposite soil carbon content from two or more of the selected quantityof locations.
 8. The method of claim 7, wherein determining thecomposite soil carbon content from two or more of the selected quantityof locations includes respectively compositing two or more layers ofequal mass of soil from the two or more of the selected quantity oflocations.
 9. The method of claim 1, wherein determining the sample soilcarbon content includes determining the sample soil carbon content by atleast one of: absolute, percentage or fractional weight or mass ofcarbon.
 10. The method of claim 1, wherein determining the total soilcarbon content includes determining the total soil carbon content in apredetermined mass of soil per unit area of the unit of land.
 11. Themethod of claim 1, wherein the total quantity of at least two strata isin a range of five to seven.
 12. The method of claim 1, whereindetermining the one or more stratum boundaries includes determining theone or more stratum boundaries based, at least partly, on the estimatedspatial distribution of soil carbon content.
 13. The method of claim 12,wherein determining the one or more stratum boundaries includesdetermining the one or more stratum boundaries based, at least partly,on a cumulative function of a square root of frequencies of occurrenceof soil carbon derived from the estimated spatial distribution of soilcarbon content.
 14. The method of claim 1, wherein the informationassociated with the unit of land with the soil carbon distribution isselected from a group consisting of: terrain information, gammaradiometric information, climate information, geologic information,regolith information, information associated with a regional predictionof spatial distribution of soil carbon content, land use classificationinformation and known soil carbon information associated with the unitof land.
 15. The method of claim 1, wherein the determination of thetotal soil carbon content is further based on a confidence interval. 16.The method of claim 1, wherein the unit of land comprises at least 400hectares associated with one carbon sequestration management contract.17. A method of quantifying soil carbon sequestered in a unit of land,the method comprising: (a) obtaining an estimated spatial distributionof soil carbon content in the unit of land by: (i) correlatinginformation associated with the unit of land with soil carbondistribution, and (ii) inputting the correlated information into a soilcarbon content prediction model to predict the estimated spatialdistribution of soil carbon content; and (b) thereafter, independentlyauditing the obtained estimated spatial distribution of soil carboncontent in the unit of land by: (i) stratifying, at least partiallybased on at least one of: a diversity of the unit of land, a land usetype, and a total area of the unit of land, the unit of land into atotal quantity of at least two strata, wherein the stratificationincludes determining one or more stratum boundaries between the totalquantity of at least two strata, the determination of the one or morestratum boundaries includes determining one or more optimum stratumboundaries under Neyman allocation, and the total quantity of at leasttwo strata is based, at least partly, on the obtained estimated spatialdistribution of soil carbon content; (ii) after stratifying the unit ofland into the total quantity of at least two strata: (1) determining aquantity of first locations to sample within each strata, the quantityof first locations to sample within each strata being at least one morethan the total quantity of at least two strata and being based, at leastpartly, on the obtained estimated spatial distribution of soil carboncontent, and (2) reducing sampling variance and fraudulent manipulationof soil carbon quantification results by randomly selecting, from eachstrata of the total quantity of at least two strata, the quantity offirst locations from that strata; (iii) using at least one of a CNSanalyser and a near infrared spectroscopic analyser, at a first time, todetermine a first sample soil carbon content associated with theselected quantity of first locations; (iv) determining first total soilcarbon content in the unit of land based, at least partly, on the firstsample soil carbon content; (v) after stratifying the unit of land intothe total quantity of at least two strata: (1) determining a quantity ofsecond locations to sample within each strata, the quantity of secondlocations to sample within each strata being at least one more than thetotal quantity of at least two strata and being based, at least partly,on the obtained estimated spatial distribution of soil carbon content,and (2) reducing the sampling variance and the fraudulent manipulationof the soil carbon quantification results by randomly selecting, fromeach strata of the total quantity of at least two strata, the quantityof second locations from that strata; (vi) using the at least one of theCNS analyser and the near infrared spectroscopic analyser, at a secondtime, to determine a second sample soil carbon content associated withthe selected quantity of second locations; (vii) determining secondtotal soil carbon content of the unit of land based, at least partly, onthe second sample soil carbon content; and (viii) determining an amountof sequestered soil carbon in the unit of land between the first timeand the second time.
 18. The method of claim 17, wherein determining theamount of sequestered soil carbon includes determining a differencebetween the first total soil carbon content and the second total soilcarbon content.
 19. The method of claim 17, wherein the informationassociated with the unit of land with the soil carbon distribution isselected from a group consisting of: terrain information, gammaradiometric information, climate information, geologic information,regolith information, information associated with a regional predictionof spatial distribution of soil carbon content, land use classificationinformation and known soil carbon information associated with the unitof land.
 20. The method of claim 17, wherein at least one of thedetermination of the first total soil carbon content and thedetermination of the second total soil carbon content is further basedon a confidence interval.
 21. The method of claim 17, wherein the unitof land comprises at least 400 hectares associated with one carbonsequestration management contract.
 22. A method of quantifying soilcarbon sequestered in a unit of land, the method comprising: (a)obtaining an estimated spatial distribution of soil carbon content inthe unit of land by: (i) correlating information associated with theunit of land with soil carbon distribution, and (ii) inputting thecorrelated information into a soil carbon content prediction model topredict the estimated spatial distribution of soil carbon content; and(b) thereafter, independently auditing the obtained estimated spatialdistribution of soil carbon content in the unit of land by: (i)stratifying, at least partially based on at least one of: a diversity ofthe unit of land, a land use type, and a total area of the unit of land,the unit of land into a total quantity of at least two strata, whereinthe stratification includes determining one or more stratum boundariesbetween the total quantity of at least two strata, the determination ofthe one or more stratum boundaries includes determining one or moreoptimum stratum boundaries under Neyman allocation, and the totalquantity of at least two strata is based, at least partly, on theobtained estimated spatial distribution of soil carbon content; (ii)after stratifying the unit of land into the total quantity of at leasttwo strata: (1) determining a quantity of first locations to samplewithin each strata, the quantity of first locations to sample withineach strata being at least one more than the total quantity of at leasttwo strata and being based, at least partly, on the obtained estimatedspatial distribution of soil carbon content, and (2) reducing samplingvariance and fraudulent manipulation of soil carbon quantificationresults by randomly selecting, from each strata of the total quantity ofat least two strata, the quantity of first locations from that strata;(iii) using at least one of a CNS analyser and a near infraredspectroscopic analyser, at a first time, to determine a first samplesoil carbon content associated with the selected quantity of firstlocations; (iv) determining first total soil carbon content in the unitof land based, at least partly, on the first sample soil carbon content;(v) re-stratifying the unit of land into a total quantity of at leasttwo re-stratified strata based, at least partly, on the first samplesoil carbon content; (vi) after re-stratifying the unit of land into thetotal quantity of at least two re-stratified strata, selecting aquantity of second locations from each strata of the total quantity ofat least two re-stratified strata, the selected quantity of secondlocations being based, at least partly, on the obtained estimatedspatial distribution of soil carbon content; (vii) using at least one ofthe CNS analyser and the near infrared spectroscopic analyser, at asecond time, to determine a second sample soil carbon content associatedwith the selected quantity of second locations; (viii) determiningsecond total soil carbon content in the unit of land based, at leastpartly, on the second sample soil carbon content; and (ix) determiningan amount of sequestered soil carbon in the unit of land between thefirst time and the second time.
 23. The method of claim 22, wherein theinformation associated with the unit of land with the soil carbondistribution is selected from a group consisting of: terraininformation, gamma radiometric information, climate information,geologic information, regolith information, information associated witha regional prediction of spatial distribution of soil carbon content,land use classification information and known soil carbon informationassociated with the unit of land.
 24. The method of claim 22, wherein atleast one of the determination of the first total soil carbon contentand the determination of the second total soil carbon content is furtherbased on a confidence interval.
 25. The method of claim 22, wherein theunit of land comprises at least 400 hectares associated with one carbonsequestration management contract.